[tex] 4y^2+2=(4y\cdot4y)+2\\
4y^2+2=16y^2+2 \leftarrow \text{not identity}\\\\
4y^2+2=(4y+y)+2\\
4y^2+2=5y+2 \leftarrow \text{not identity}\\\\
4y^2+2=4(y+y)+2\\
4y^2+2=8y+2 \leftarrow \text{not identity}\\\\
4y^2+2=4(y\cdot y)+2\\
4y^2+2=4y^2+2 \leftarrow \text{identity}[/tex]
So it's D.